Evidence for Duality of Conifold from Fundamental String

TL;DR

This paper provides strong evidence for string duality on the conifold by matching BPS state spectra in type IIB and type IIA theories using partition functions and wall-crossing formulas.

Contribution

It demonstrates the duality between D5-D3-F1 states in type IIB and D4-D2-D0 states in type IIA on the conifold by explicit partition function comparison.

Findings

BPS partition functions match across dual theories.

Results hold for all moduli values.

Supports the conjecture of conifold duality.

Abstract

We study the spectrum of BPS D5-D3-F1 states in type IIB theory, which are proposed to be dual to D4-D2-D0 states on the resolved conifold in type IIA theory. We evaluate the BPS partition functions for all values of the moduli parameter in the type IIB side, and find them completely agree with the results in the type IIA side which was obtained by using Kontsevich-Soibelman's wall-crossing formula. Our result is a quite strong evidence for string dualities on the conifold.